| Dependence measures | copula_dependence | Kendall’s tau, Spearman’s rho, Pearson, Blomqvist’s beta, Hoeffding’s D and Chatterjee’s xi matrices between assets, implied copula parameters, tail dependence from pairwise copulas, pseudo-observations, quasi-random uniform samples and latent samples for discrete pairs. | 5 |
| Margins and joint distributions | copula_distribution | Univariate margins (boundary-corrected kernel densities for continuous, discrete and zero-inflated data, or the best parametric family by AIC/BIC/AICc, or a density given on a grid) and joint distributions of many assets combining margins with a vine copula: density, joint probabilities, Rosenblatt transforms and samples on the original scale. | 2 |
| Bivariate copulas | copula_pair | Copulas for two assets: fit a chosen family and rotation or select the best of every family (Gaussian, Student, Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7, BB8, Tawn, nonparametric TLL) by AIC/BIC/mBIC, compare families, parameter standard errors; densities, distribution and h-functions with their inverses and derivatives; simulation; tau, Blomqvist beta and tail-dependence conversions. | 5 |
| Vine regression | copula_regression | Conditional mean and quantiles of one asset given others from a vine copula with kernel margins: nonlinear, tail-aware regression such as a stock’s 5% quantile given the market (CoVaR-style). | 1 |
| Copula portfolio risk | copula_risk | Portfolio value at risk and expected shortfall from vine-copula scenarios mapped through each asset’s empirical, kernel or parametric margin, with Gaussian-copula and historical benchmarks and expected shortfall contributions; stress scenarios that hold chosen assets at a shock and draw the rest from their conditional distribution. | 2 |
| Vine copulas | copula_vine | Vine copulas for many assets: R-vine structure selection (maximum or random spanning trees on Kendall’s tau, Spearman, Hoeffding, Chatterjee or mutual information), C- and D-vines, given matrices, truncation, thresholding, family sets and criteria; structures built by hand; density, distribution, Rosenblatt and inverse Rosenblatt transforms, per-edge contributions, parameter inference; unconditional and conditional simulation. | 4 |
